Verified answer

Hello!

√-3 * √-27

Breaking that down into:

i√3 * i√27

This gives us:

i^2√81

==> i^2 * 9

==> -1 * 9

==> -9

Our answer is A.

I hope this helps!

Sincerely,

Mr.Math

The correct answer is a, -9. This is a good example of a trap you can easily fall into when dealing with complex numbers. For positive real numbers a and b it is always true that

√a times √b = √ab.

However this is not true if you let a and b be general complex numbers (for example negative numbers). If it were you would have

-1 = i^2 = √-1 times √-1 = √1 = 1

which is wrong.

a negative in a radical is the same as a positive because a + times a += a + and a - times a -= a positive. so sq root of 3 x sq root of 27=sq root of 81= 9

a. the answer is -9

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√(-3) *√(-27) = i√(3) *i√(27)

                  = i²√(81)

                  = -1√(81)

                  = -9

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